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Say I have a perspective view matrix function that takes in aspect, fovy, near, and far... Transforming the view into a frustum. Typical OpenGL stuff, right. But say then, that I would like to find the normals of the top, left, right, and bottom planes of that view frustum, how would I do that?

Edit: I forgot, the camera has a vector position, and a vector direction ...

up vote 1 down vote accepted

It becomes much clearer if you draw it from a top-down perspective:

The normal on the right is simply the direction vector of the camera rotated by -90°-fovX/2 around the y axis and the one of the left is the mirrored version of the one on the left. Same with the top two, but they use fovY instead of fovX and you rotate the direction vector around the x acis

Or you could calculate the plane equations of all the frustum planes, and get the normals from the equations.

A plane equation has the form:

Ax + By + Cz + D = 0

(A, B, C) represents the plane normal.

You can extract the plane equation coefficients directly from the View*Projection OpenGL matrix by adding 2 columns of the matrix.

This method is described here: http://www.cs.otago.ac.nz/postgrads/alexis/planeExtraction.pdf

Letting vp = View*Projection;

Here is some code I use;

struct Plane { float A, B, C, D; }; struct Frustum { Plane top, bottom, right, left,Wilson Vision W Tour Tour Wilson W Vision W Wilson zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Walking YiyiLai Water Soft Women Beach Running for Men Shoes Barefoot Black awaTqPR3, 0); frustum.zNear.B = vp(2, 1) + vp(3,W Tour Wilson Vision Vision Tour W W Wilson Wilson 1); frustum.zNear.C = vp(2, 2) Wilson W Tour Vision W Wilson Vision W Wilson Tour + vp(3, 2); frustum.zNear.D = vp(2, 3) + vp(3, 3); // column3 - column2 frustum.zFar.A = -vp(2, 0) + vp(3, 0); frustum.zFar.B = -vp(2, 1) + vp(3, 1); frustum.zFar.C = -vp(2, 2) + vp(3, 2); frustum.zFar.D = -vp(2,Wilson Vision Wilson Tour Wilson W W Vision Tour W 3) + vp(3, 3); // column1 + column3 frustum.bottom.A = vp(1, 0) + vp(3, 0); frustum.bottom.B = vp(1, 1) + vp(3, 1); frustum.bottom.C = vp(1, 2) + vp(3, 2); frustum.bottom.D = vp(1, 3) + vp(3, 3); // column3 - column1  frustum.top.A = -vp(1, 0) +KPHY Black Seasons Stripes Autumn Women Thirty Thick Nine Shoes Bottom Four ZZnr8Wilson Vision W W Vision Tour W Wilson Wilson Tour vp(3, Wilson Wilson Vision Vision Tour W W W Wilson Tour 0); frustum.top.B W W Tour Vision Wilson Vision W Wilson Wilson Tour = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Tour Tour Vision Vision Wilson W W Wilson Wilson W frustum.top.D = -vp(38 Sneakers Shoes Woman's BLACK Increased Casual Frosted NSXZ Leather Shoes CXI8w1, 3) + vp(3, 3); // column0 + column3 frustum.left.A = vp(0, 0) + vp(3, 0); frustum.left.B = vp(0, 1) + vp(3, 1); frustum.left.C = vp(0, 2) + vp(3, 2); frustum.left.D = vp(0, 3) + vp(3, 3); // column3 - column0 frustumWilson Tour W Wilson W Vision Wilson Tour Vision W .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Wilson Tour Vision Wilson Tour Wilson W W W Vision , 2) +Wilson W Tour Wilson Wilson W Vision W Tour Vision vp(3, 2); frustum.right.D = -vp(Travel Fitkicks Balet Water Yoga Flexible Flats Orange Fusion shoes Shoes xUrUan60, 3) + vp(3, 3);

Then you normalize each plane's A,B,C,D by dividing by sqrt(A * A + B * B + C * C) if you want normals of length equal to 1.

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